Drawing instrument

ABSTRACT

This instrument is a drawing instrument for drafting axonometric projection drawings based on a projection drawn by the multiview projection, with which any of projection drawings, either isometric, dimetric or trimetric, may be produced by the operations of rulers.

United States Patent 1191 Hirano 51 Feb. 25, 1975 1 DRAWING INSTRUMENT[76] Inventor: Akira Hirano, 178 Kashira-machi,

i1lla as11tna K mi wr u 2119191 Japan 221 Filed: July 14,1972

21 Appl. No.: 271,646

[30] Foreign Application Priority Data July 14, 1971 Japan 46-52340 July14, 1971 46-52337 July 14, 1971 46-52338 July 14, 1971 Japan 46-52339[52] US. Cl. 33/77 [51] Int. Cl ..B43l13/14 [58] Field of Search..'33/77, 18 C [56] References Cited UNITED STATES PATENTS 2,454,38011/1948 Goff 33/79 R FOREIGN PATENTS OR APPLICATIONS 1,008,492 5/1957Germany 33/77 465,199 9/1928 Germany 33/79 R 761,930 11/1950 Germany33/77 Primary Examiner-Harry N. Haroian Attorney, Agent, orFirm-Armstrong, Nikaido & Wegner [57] ABSTRACT This instrument is adrawing instrument for drafting axonometric projection drawings based ona projection drawn by the multiview projection, with which any ofprojection drawings, either isometric, dimetric or trimetric, may beproduced by the operations of rulers.

3 Claims, 6 Drawing Figures 8/1972 Heinz 33/77 DRAWING INSTRUMENTBACKGROUND OF THE INVENTION The hitherto considered method of drafting aaxonometric projection drawing from the multiview projection drawings,consists of the assumption of a cube 1 having two faces X and Y whichintersect at a right angle, and are perpendicular to three straightlines, OX, OY and OZ. The faces X, Y and Z are arranged parallel tothefront, plan and side faces of the body, and the multiview projectiondrawings including the front view A, plan view B, etc., may be drawnwith the ridge XO as the ground line by projecting the beam lines on theprojecting faces at a right angle respectively. On the other hand, thepiramidal part with the apex O of the cube is cut off, and with this cutface XYZ taken as the new projecting face, the axonometric projectiondrawing C of the central body is drawn by projecting the beam lines onthis face at a right angle thereto. According to a geometrical theory,the lines connecting the corresponding points on the front view A or theplan view B with the corresponding points on the axonometric projectiondrawing criss-cross the ridges XZ, XY of the cut face, which may,therefore, be regarded as the ground lines. Accordingly, as the planesof the front view and the plan view are turned upward, they are centeredon the ground lines of the cut face to the same plane as that of theprojecting face of the cut face XYZ, and projecting lines are drawnperpendicular to the respective ground lines from each apex (a, b h) ofthe front view and plan view, thus the intersections reasonably agreewiththe corresponding points of the axonometric projection C.

Accordingly, to draw an axonometric projection drawing, usually theground line XY and X2 which make a certain intersecting angle K areassumed, as shown in FIG. 6; the front view A and the plan view B, arearranged at certain angles (described later) to the ground lines X2 andXY; and a perpendicular m is drawn from the front view A to the groundline XZ, and another perpendicular 1,, from the plan view B, to theground line XY; then, by plotting the intersections, the axonometricprojection is drawn.

In this method, however, the intersecting angle K of the axes X2 and XYof the projecting triangle and the way of arranging the front view A andthe plan view B, relative to the ground lines XZ and XY are not fullyascertained. First, the intersecting angle K is determined by theconditions, or six factors, to define the cube having X, Y and Z faces,as shown in FIG. 5; that is, the angles )t, p. and 7 which the beamlines make with respective faces of the cube, and the angles a, B and 7which the bottom sides of the projected figures on respective faces makewith the ground lines XY, X2 and YZ. In the next place, referring toFIG. 5, as the three axes OX, CY and OZ which mutually criss-cross aretransferred to the projecting face XYZ, then the three straight lines X,O Y and 0,2 which intersect at a point 0, corresponding to the apex Oare respectively perpendicular to their opposing sides, according to thegeometrical theory. Accordingly, as the plane XYO is turned, andcentered on the axis XY, to align with the projecting face XYZ, the apex0 moves on the aforementioned perpendicular ZO to the point 0 Thisoperation is reproduced on the projecting face XYZ in FIG. 6. Theorthocenter 0 of the triangle XYZ is the projected point of the apex 0.If the intersection between the circle with the side XY as its diameterand the perpendicular ZZ from the apex Z is designated 0 then [XO Y is 0is, therefore, the point transferred from the former apex O of the cubeby the rotary motion. Accordingly, since 0 X corresponds to the groundline OX of the Z face of the cube on the plan view B, of the Z facerotated, the side dc of the plan view B, is arranged in parallel to O Xwith this 0 X as the ground line. A similar operation is carried outwith the Y face, so that the projecting point 0 of I the apex Otransferred by rotation with XZ as the axis is determined in thetriangle XYZ. Then, as X0 corresponds to the ground line X0, the side abof the front view A is arranged parallel to the straight line X0 Afterthese arrangements are made, projecting lines I and m are drawn to theground lines XY and XZ, thereby obtaining the respective intersections.In this way, the axonometric projection intended is obtained.

In the usual'method, the front view A and the plan view B should beseparated, arranged around the face of the axonometric projection, andinclined at certain angles. Since in the actual multiview projection,the front view and the plan view B are drawn on one sheet of paper inparallel to each other, many inconveniences are involved in separatingand arranging them as described above.

The plan view B was drawn in parallel to the front view A on the commonplane of axonometric projection, as shown in FIG. 6. As the projectingline 1 of the former plan view B, was drawn, it was fixed to the figureunmodified, on the basis of the assumption that the plan view B wasformed by rotating and transferring, on the same surface of the paper,the aforementioned plan view B arranged with an inclination to the mainaxis XY. Then, it was discovered that the projecting lines I drawn fromthe FIG. B intersect the projecting lines 1,, drawn from the FIG. B onthe same straight line P, and the projecting lines I and 1,, intersecteach other as if they were light beams reflecting from the straight lineP as the mirror surface with the angle of incidence and reflection at 0(the substantiation for this is omitted).

The present invention concerns a drawing instrument capable of makingthe drawing of axonometric projection by way of ruler operations andmanipulations while placing the front view A and the plan view arrangedvertically, and taking advantage of the aforementioned principle.

SUMMARY OF THE INVENTION The present invention makes it possible todraft the axonometric projection in such a way that with the front viewand the plan view arranged vertically, and the straight line P making apredetermined angle with the ground line and the direction of theprojecting lines m from the front view known, the projecting lines I canbe drawn out from the plan view B at a given angle to the straight lineP; these lines are reflected at the straight line P to form theprojecting lines 1 and the corresponding points on the axonometricprojection are determined by their intersection with the projectinglines from the front view.

The object of the present invention is to provide a drawing instrument,with which it is possible to draft an axonometric projection from amultiview projection drawn side by side by rotating the rulers arrangedand oriented of appropriate angles, and combining these rulers with anangular ruler.

Another object of the present invention is to provide a drawinginstrument with the third ruler attached in addition to the vertical andhorizontal rulers to facilitate the operation of making the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS:

FIG. 1 illustrates a total plan view of one embodiment'of the invention,showing the device in a drafting operation;

FIGS. 2 and 3 respectively illustrate enlarged plan views of the deviceas arranged and oriented in other embodiments;

FIG. 4 illustrates a plan view showing another application of thedrawing instrument of FIG. 3;

FIG. 5 illustrates a perspective view for demonstrating the principle ofthe axonometric projection; and,

FIG. 6 illustrates another explanatory diagram of the principle of thisinvention.

DETAILED DESCRIPTION The drawing instrument which has been well known upto present is utilized in making up the drawing instrument of thisinvention. The drawing instrument 2 (as shown in FIG. 2) of FIG. 1 isshown with the ruler orienting element 5 of the drawing instrument 2 ofFIG. 2 being enlarged. To this element 5, is attached ruler element 5Aand the horizontal ruler 3 and the vertical ruler 4 are attached at itstip. It is equipped with the angle changing mechanism 7 with which thehorizontal ruler 3 is inclined at an appropriate angle by switching thelever 6, and then, the element 5 is clamped and the parallel transfermechanism 9 connecting the element 5 to the fixed point 8 through linksof parallelograms, with which the horizontal ruler 3 and the verticalruler 4 are transferred in parallel to themselves as shown by thephantom lines in FIG. 1.

The standard line 10 is marked at the tip of the vertical ruler 4. Itsroot end is pivotally mounted for rotation on the pivot 11 of the rulerelement 5A. It is clamped with a fixing means 12, inclined at a certainangle q to the horizontal ruler 3.

The horizontal ruler 3 is extended from the element 5A, and theauxiliary ruler 13 is attached to it on the same line in a linearfashion. An angular ruler 14 is located at a definite point on thesurface of this auxiliary ruler, making a certain angle p to the-rulersurface. This angular ruler 14 may be located so as to rotate along withthe auxiliary ruler so that it may be brought down normally andmaintained flush with the auxiliary ruler, and thus is used by drawingit out to the angle p and holding it. Alternatively, as shown in thedrawing, the same purpose may be served by detachably providing atriangular ruler 15 with one of its base angles p. In this instance, thestopper 16 by which thetriangular ruler 15 is held in place on thehorizontal ruler 3 is provided, so that the projecting line may be drawnat the angle of p-from a definite point on the auxiliary ruler 3.

In the following, the drafting procedure is described for this draftingfrom the front view and plan view of FIG. 1 drawn by the first quarterdrawing method:

1. First, after slackening the lever 6 of the drawing instrument 2, thestandard line P making a certain angle t with the central line T of thefront view A is drawn.

2. With the horizontal ruler 3 put to 12 point of the front view A, theprojecting line m is drawn along the auxiliary ruler I3.

3. The ruler face of the vertical ruler 4 is put to h point of the planview B, and simultaneously, the standard line 10 of the vertical ruler 4is brought in line with the standard line P. I

4. The vertical ruler 4 is securely held in that position, and thetriangular ruler I5 is placed on the auxiliary ruler 13, with one end ofthe triangular ruler l5 touched on the stopper l6.

5. The projecting line 1,, is drawn at an angle of p along the rulerface of the triangular ruler l5.

6. The intersection b between the projecting line 1,, and the projectingline m is the desired point on the view of axonometric projection. Otherpoints are determined in the same way to draw up the projection draw-Referring to FIG. 6, the projecting angle a agrees with LO1XY, with itsactual angle a, given by LO2XY, while the projecting angle ,8 agreeswith L OIXY, with its actual angle b given by L O3XZ.

The angle at which the projecting line I from the plan view B isreflected at the standard line P, designated 26, is identical with theangle of rotation of the plan view B to the plan view B.

Assuming that the intersecting angle between the projecting lines I andm is r, and the intersecting angle between the projecting line I and thecentral line T is s, then r= a and s b as geometrically proven. Thereexists a relation, 4) a 0, and p agrees with 4ZXY.

In the case of equiangular projection, a 45, b 4 31 4Z Y= Qf b9r 0=. "141= s P 60, and q 90. Accordingly, the purpose may be served by use of atriangular ruler 15 with its interior angles 90, 60 and 30.

The drafting of the axonometric projection drawing can be accomplishedby the drafting procedure mentioned above. The projection drawing C maybe drawn from the front view A and the plan view B drawn by the thirdquarter drawing method in the same way as in FIG. 3.

The angles p, q and t employed in the drafting performed as describedabove are preliminarily given as the drafting conditions, that is,conditions defined by the angles k, v and p. that the beam line makeswith the X, Y and Z faces of the cube and the angles a, B and y whichthe axonometrical projection drawing of a solid body'makes with theground line.

Since in the case of an equiangular projection drawing, the angle qwhich the vertical ruler 4 makes with the horizontal ruler 3 is a rightangle, an ordinary drawing instrument manufactured with both rulersfixed at a right angle may be put to this use.

In FIG. 2, the standard line 17 is drawn at the tip of the verticalruler 4 at an angle of (b which the standard line P makes with the rulerface, or desirably at 4) 60 which is assigned for the equiangularprojection drawing, and the standard line 17 is aligned with thestandard line P, while the horizontal ruler 3 is put to the front view,and simultaneously, the projecting line m is drawn, whereby theauxiliary ruler is omitted.

FIG. 3 presents another embodiment of this invention, in which while thevertical ruler 4 is fixed perpendicular to the horizontal ruler 3 as inFIG. 2, the auxiliary ruler 13 is rotatably attached at its root end onthe opposite side of the horizontal ruler 3. Angular ruler 14 isslidably located along auxiliary ruler 13 with reference to stopper 20.When the auxiliary ruler l4 and the horizontal ruler 3 are arranged onthe same straight line, that is at the orientation angle of this drawinginstrument may be used for drafting an equiangular projection drawing.Then, when element 5 is reversed by 180, and the auxiliary ruler isinclined at an angle of 6 as shown in FIG. 4, a reduced drawing from theoriginal one may be produced. That is, when the horizontal line a b ofthe original drawing D is arranged parallel to the auxiliary ruler l3,and the standard line 18 on the auxiliary ruler 13 is transferred from ato b and from a to d,, the triangular ruler 19 is placed on thehorizontal ruler 3, and then, the points corresponding to those on thevertical and horizontal lines are plotted, thereby drafting the reduceddrawing E from the FIG. A. This may be proven as follows. Perpendicularsare drawn respectively from points b and a to the straight line Dpassing through a of the figure D and parallel to the ruler, aand theirintersections are designated b and d Then, the horizontal distance a bon the FIG. E corresponding to the horizontal distance a b on theoriginal FIG. D is:

a b a b a b cos 0.

Similarly, the vertical distance a d on the FIG. E corresponding to thevertical distance a d on the original FIG. D is:

z z 11 111 11 d, cos 0 Accordingly, the FIG. E is reduced from theoriginal figure D in dimension for each side by cos 0,. It is alsopossible to draft the enlarged figure D with the figure E as theoriginal by turning the element 5 by 180.

1 claim:

1. A drawing instrument for use in drafting the anonometric projectiondrawing from the multiview projection drawing, comprised of thefollowing components;

a. a parallel transferring mechanism with which a ruler orienting andarranging means is transferred parallel to itself and the angle changingmechanism with which the ruler arranging means angle is altered;

b. a horizontal ruler attached to the arranging means of the drawinginstrument;

0. a vertical ruler attached to the arranging means of the drawinginstrument at a right angle to the horizontal ruler and provided withthe standard line extending traversely thereof near the free end andmaking an angle of inclination of to the ruler edge face, said verticalruler having a stopper member located thereon near the arranging means;

d. an auxiliary rulerpivotally mounted on an end of said arranging meansfor independent rotation relative to said vertical and horizontalrulers, the position of said pivotal mounting being at a location'onsaid arranging means remote from said attachment of said horizontal andvertical rulers such that they extend in substantially oppositedirections;

e. an angular ruler arranged to sliding engage said horizontal ruler andsaid stopper for drawing a line at a certain angle from a definite pointon the ruler face and located adjacent to said auxiliary ruler andslidable therealong.

2. A drawing instrument, as defined in claim 1, wherein the angularruler is a triangular ruler with its base and legs at predeterminedangles, and adapted to function with the stopper.

3. A drawing instrument, as defined in claim 2, wherein the triangularruler has interior angles of 30, 60 and

1. A drawing instrument for use in drafting the anonometric projectiondrawing from the multiview projection drawing, comprised of thefollowing components; a. a parallel transferring mechanism with which aruler orienting and arranging means is transferred parallel to itselfand the angle changing mechanism with which the ruler arranging meansangle is altered; b. a horizontal ruler attached to the arranging meansof the drawing instrument; c. a vertical ruler attached to the arrangingmeans of the drawing instrument at a right angle to the horizontal rulerand provided with the standard line extending traversely thereof nearthe free end and making an angle of inclination of 75* to the ruler edgeface, said vertical ruler having a stopper member located thereon nearthe arranging means; d. an auxiliary ruler pivotally mounted on an endof said arranging means for independent rotation relative to saidvertical and horizontal rulers, the position of said pivotal mountingbeing at a location on said arranging means remote from said attachmentof said horizontal and vertical rulers such that they extend insubstantially opposite directions; e. an angular ruler arranged tosliding engage said horizontal ruler and said stopper for drawing a lineat a certain angle from a definite point on the ruler face and locatedadjacent to said auxiliary ruler and slidable therealong.
 2. A drawinginstrument, as defined in claim 1, wherein the angular ruler is atriangular ruler with its base and legs at predetermined angles, andadapted to function with the stopper.
 3. A drawing instrument, asdefined in claim 2, wherein the triangular ruler has interior angles of30*, 60* and 90*.